How can I add "trim" to a curved surface?
It's a shame Blender doesn't directly have an 'Offset Even' tool, along  the perpendiculars to the edges being offset. A 2D curve can do it, so you could start with the trim, and build the plate away from it.. but starting with the plate as a mesh...

.. the E 'Even' option in the  GG edge-slide tool means 'even along the crossing edge-rings', not a perpendicularly even distance from the loop itself. The illustration shows a sort of worst-case, with all the crossing edges vertical, so their density changes across the width. A simple  GG (above) doesn't work.
If you're building the trim outwards from the plate, you could:

Extrude the edges to be trimmed towards the center of curvature of the plate, like the rim of a Solidify modifier..
AltE Extrude the new rim faces outward along their normals
Delete the surplus faces.

This method. though, builds the trim inwards.

As in 1. above, extrude the curve to be trimmed (top, in the picture below). This extrusion won't do anything except to tell the next operator what to do..



.. Which is I inset the region of all the faces in the original plate, with 'Even' checked, no 'Edge Rail', and no 'Boundary' inset. (Bottom, above).
The extruded faces have done their job, helping a selective inset, and can be deleted.



The new border-strip of faces can now be AltE extruded along its normals.

(I've had to tidy up the inside of the plate a bit, reconnecting the top and bottom with Bridge Edge Loops .. the topology inside your plate looks better than this, from what I can see)
Add a Bevel by angle modifier, and a Subdivision Surface..

The edge-lengths do check out.. they're pretty much the same all the way along the trim.